Please place test corrections on desk Warmup: Graph f(x) = 4 + log3 (x+2) Check using document camera Check Homework using document camera Return Quiz 1 Go over Quiz 1 using doc camera

Introduction to Compound Interest: a Develop Task M3U3D5 Introduction to Compound Interest: a Develop Task Objective: Write expressions in equivalent forms to solve problems. Essential Question: How can we use logarithms to solve exponential equations involving compound interest?

Turn to page 29. Work pages 29-31 WITH Students

Let’s summarize the properties we discovered and add a few more.

NOTICE!!! 20 = 1 Log2 1 = 0 21 = 2 Log2 2 = 1 22 = 4 Log2 4 = 2 23 = 8 Log2 8 = 3 24 = 16 Log2 16 = 4 25 = 32 Log2 32 = 5

Properties of Logarithms There are four basic properties of logarithms that we have been working with. For every case, the base of the logarithm can not be equal to 1 and the values must all be positive (no negatives in logs)

Change of Base Formula Example log58 = This is also how you graph in another base. Enter y1=log(8)/log(5). Remember, you don’t have to enter the base when you’re in base 10!

Product Rule logbMN = logbM + logbN Ex: logbxy = logbx + logby Ex: log6 = log 2 + log 3 Ex: log39b = log39 + log3b

Quotient Rule

Power Rule

These next two problems tend to be some of the trickiest to evaluate. Actually, they are merely identities and the use of our simple rule will show this.

Example 1: Solution: First, we write the problem with a variable. Now take it out of the logarithmic form and write it in exponential form.

Example 2: Solution: First, we write the problem with a variable. Now take it out of the exponential form and write it in logarithmic form.

If Loga ab = y then y = b AND… Ask your teacher about the last two examples. They may show you a nice shortcut. If Loga ab = y then y = b AND… If aLoga b = y then y = b

Finally, we want to take a look at the Property of Equality for Logarithmic Functions. Basically, with logarithmic functions, if the bases match on both sides of the equal sign , then simply set the arguments equal.

Example 3: Solution: Since the bases are both ‘3’ we simply set the arguments equal.

Example 4: Solution: But we’re not finished… Solution: Since the bases are both ‘8’ we simply set the arguments equal. Factor Solution: But we’re not finished…

Example 4 continued… It appears that we have 2 solutions here. If we take a closer look at the definition of a logarithm however, we will see that not only must we use positive bases, but also we see that the arguments must be positive as well. Therefore -2 is not a solution. Let’s end this lesson by taking a closer look at this.

Our final concern then is to determine why logarithms like the one below are undefined. Can anyone give us an explanation ?

Example 5: One easy explanation is to simply rewrite this logarithm in exponential form. We’ll then see why a negative value is not permitted. First, we write the problem with a variable. Now take it out of the logarithmic form and write it in exponential form. What power of 2 would gives us -8 ? Hence expressions of this type are undefined.

Classwork: p. 29-31 Homework: p. 25 #1-6 all,